Doctor of Philosophy / Department of Physics / Itzhak Ben-Itzhak / Present laser technology allows for the production of ultra short (&7 fs) intense (.1016 W/cm2)pulses, which are comparable in duration and interaction strength to the vibrational period and the interaction that binds the electron in molecules, respectively. In this intense-field ultra short-pulse regime one can both measure and manipulate dynamics on the femtosecond timescale. To probe the dynamics of laser-matter interactions in this regime, we have chosen to start from the simplest possible molecule - H+ 2 , which can either dissociate into H + p or ionize into p + p + e. We have designed and employ a coincidence three-dimensional momentum imaging technique which allows us to measure ionization and dissociation of a molecular ion beam target simultaneously, while completely separating the two channels from each other. By varying the laser intensity and the pulse duration, we measure the intensity and pulse length dependent momentum distributions for laser induced fragmentation of H+ 2 at 790 nm. These dissociation measurements are in agreement with the phenomena predicted using the adiabatic Floquet picture, e.g. bond softening, in addition to more sophisticated calculations done by solving the time-dependent Schrodinger equation in the Born-Oppenheimer representation. Furthermore, the structure seen in ionization in our measurements and soon after by others is explained via a unified diabatic Floquet picture, which includes both ionization and dissociation in a single intensity and wavelength dependent picture that includes nuclear motion. Additionally, we use the same experimental techniques and apparatus to probe the laser-induced dynamics of multi-electron diatomic molecules, e.g. O+2, N+2, and ND+. The most probable dissociation and ionization pathways producing the features seen in these measurements are discerned using the angular and kinetic-energy-release distributions in conjunction with the diabatic Floquet picture. Finally, we extend these experimental techniques and interpretive models to the simplest polyatomic molecule - H+ 3 , whose fragmentation presents challenges both in our first-of-their-kind experiments and in physical interpretation.